We have studied the low temperature photoluminescence (PL) of the two-dimensional electron gas in a 100 Angstrom quantum well at fields up to 50 T over four orders of magnitude of laser power. At our highest laser powers we observe excitonic recombination via neutral and negatively charged (X-) excitons, and determine the X- binding energy to fields of 50 T. The binding energies of both singlet and triplet states increase monotonically with field above 15 T. At lower laser powers, in which recombination from the second Landau level is observed at fields up to 2.5 T, a splitting appears at high fields (>10 T) due to the recombination from the singlet and triplet states of X-. These data are inconsistent with a universal transition from free-carrier to excitonic recombination at Landau-level filling factor v=2, but imply that the onset of excitonic recombination is dependent on the illumination conditions.